EXHIBIT 32

                CERTIFICATION PURSUANT TO 18 U.S.C SECTION 1350,
                                  AS ENACTED BY
                  SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

In connection with Third Wave Technologies, Inc. (the "Company) Form 10-Q for
the period ended September 30, 2004 as filed with the Securities and Exchange
Commission on the date hereof (the "Report"), John Puisis, Chief Executive
Officer of the Company, and David Nuti, Chief Financial Officer of the Company,
certify, pursuant to 18 U.S.C Section 1350, that:

      (1) The Report fully complies with the requirements of section 13(a) or
15(d) of the Securities Exchange Act of 1934; and

      (2) The information contained in the Report fairly presents, in all
material respects, the financial condition and result of operations of the
Company.

                                              /s/ John Puisis
                                              -------------------------------
                                              John Puisis
                                              Chief Executive Officer
                                              October 29, 2004

                                              /s/ David Nuti
                                              -------------------------------
                                              David Nuti
                                              Chief Financial Officer
                                              October 29, 2004

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